Bootstrap methods for digitized scalar field theory (2312.10559v1)
Abstract: General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the matrix elements. These recursive methods are derived by looking at the commutation relations of the observables with the Hamiltonian. We discuss how this self-consistent (bootstrap) approach can be applied to the study of digitized scalar field theory in the harmonic basis. Using known results, we develop the method by testing on quantum systems, including the harmonic and anharmonic oscillators. We report recent numerical results for up to four coupled anharmonic oscillators. From here, we consider the possibility of using the groundwork of this method as a means of studying phase transitions in 1+1 dimensions.
- Quantum Algorithms for Quantum Field Theories. Science, 336:1130–1133, 2012.
- Digitization of scalar fields for quantum computing. Phys. Rev. A, 99:052335, 2019.
- Digital quantum computation of fermion-boson interacting systems. Phys. Rev. A, 98:042312, 2018.
- Robert Maxton, Yannick Meurice. Perturbative boundaries of quantum advantage: real-time evolution for digitized λϕ4𝜆superscriptitalic-ϕ4\lambda\phi^{4}italic_λ italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT lattice models. Phys. Rev. D, 107:074508, 2023.
- Y. Meurice. A Simple method to make asymptotic series of Feynman diagrams converge. Phys. Rev. Lett., 88:141601, 2002.
- Xizhi Han, Sean A. Hartnoll and Jorritt Kruthoff. Bootstrapping Matrix Quantum Mechanics. Phys. Rev. Lett, 125:041601 2020.
- David Berenstein, George Hulsey. Bootstrapping Simple QM Systems. arxiv:2108.08757v2.
- H. Araki. Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field Theory Journal of Math. Phys. 492: 10.1063/1.1703685, 1960.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.